Closed embeddings into Lipscomb's universal space

Let J(τ) be Lipscomb\u27s one-dimensional space and Ln(τ) = {x J(τ)n+1 | at least one coordinate of x is irrational} J(τ)n+1 Lipscomb\u27s n-dimensional universal space of weight τ ≥ אo. In this paper we prove that if X is a complete metrizable space and dim X ≤ n, w X ≤ τ, then there is a closed embedding of X into Ln(τ). Furthermore, any map f : X → J(τ)n+1 can be approximated arbitrarily close by a closed embedding ψ : X → Ln(τ). Also, relative and pointed versions are obtained. In the separable case an analogous result is obtained, in which the classic triangular Sierpinski curve (homeomorphic to J(3)) is used instead of J(אo)